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Mat. Sb., 1994, Volume 185, Number 8, Pages 81–102 (Mi msb919)  

This article is cited in 28 scientific papers (total in 28 papers)

On approximation by families of linear polynomial operators in $l_P$-spaces, $0<p<1$

K. V. Runovskii

T. H. Shevchenko Chernihiv State Pedagogical Institute

Abstract: New applications are given for a method of approximation by families of linear polynomial operators in $L_p$-spaces with $0<p<1$ that was developed by the author in previous papers. In particular, a direct theorem and an inverse theorem on approximation 'by angle' of trigonometric polynomials are proved in the case of higher-order moduli of smoothness.

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English version:
Russian Academy of Sciences. Sbornik. Mathematics, 1995, 82:2, 441–459

Bibliographic databases:

UDC: 517.51
MSC: Primary 41A10, 41A27, 41A63, 42A10; Secondary 41A50, 42B99
Received: 27.09.1993

Citation: K. V. Runovskii, “On approximation by families of linear polynomial operators in $l_P$-spaces, $0<p<1$”, Mat. Sb., 185:8 (1994), 81–102; Russian Acad. Sci. Sb. Math., 82:2 (1995), 441–459

Citation in format AMSBIB
\by K.~V.~Runovskii
\paper On approximation by families of linear polynomial operators in $l_P$-spaces, $0<p<1$
\jour Mat. Sb.
\yr 1994
\vol 185
\issue 8
\pages 81--102
\jour Russian Acad. Sci. Sb. Math.
\yr 1995
\vol 82
\issue 2
\pages 441--459

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    This publication is cited in the following articles:
    1. N. N. Pustovoitov, “Estimates of the best approximations of periodic functions by trigonometric polynomials in terms of averaged differences and the multidimensional Jackson's theorem”, Sb. Math., 188:10 (1997), 1507–1520  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. Burinska Z., Runovski K., Schmeisser H., “On the Method of Approximation by Families of Linear Polynomial Operators”, Z. Anal. ihre. Anwend., 19:3 (2000), 677–693  mathscinet  zmath  isi
    3. Ditzian Z., Runovskii K., “Realization and Smoothness Related to the Laplacian”, Acta Math. Hung., 93:3 (2001), 189–223  crossref  mathscinet  zmath  isi
    4. S. B. Vakarchuk, “Exact Constants in Jackson-type Inequalities and Exact Values of Widths”, Math. Notes, 78:5 (2005), 735–739  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. Runovski K., Rystsov I., Schmeisser H.-J., “Computational Aspects of a Method of Stochastic Approximation”, Z. Anal. ihre. Anwend., 25:3 (2006), 367–383  crossref  mathscinet  zmath  isi
    6. Konstantin Runovski, Hans-Jürgen Schmeisser, “On Approximation Methods Generated by Bochner-Riesz Kernels”, J Fourier Anal Appl, 14:1 (2008), 16  crossref  mathscinet  zmath  isi
    7. K. Runovski, H.-J. Schmeisser, “On convergence of families of linear polynomial operators generated by matrices of multipliers”, Eurasian Math. J., 1:3 (2010), 112–133  mathnet  mathscinet  zmath
    8. V. I. Ivanov, “Direct and inverse theorems in approximation theory for periodic functions in S. B. Stechkins papers and the development of these theorems”, Proc. Steklov Inst. Math. (Suppl.), 273, suppl. 1 (2011), S1–S13  mathnet  crossref  elib
    9. K.  Runovski, H.-J. Schmeisser, “On families of linear polynomial operators generated by Riesz kernels”, Eurasian Math. J., 1:4 (2010), 124–139  mathnet  mathscinet  zmath
    10. F. Dai, Z. Ditzian, “Jackson theorem in , for functions on the sphere”, Journal of Approximation Theory, 162:2 (2010), 382  crossref
    11. Vladimir Rukasov, Konstantin Runovski, Hans-Jürgen Schmeisser, “Approximation by families of linear trigonometric polynomial operators and smoothness properties of functions”, Math. Nachr, 2011, n/a  crossref
    12. M. Sh. Shabozov, G. A. Yusupov, “Exact constants in Jackson-type inequalities and exact values of the widths of some classes of functions in $L_2$”, Siberian Math. J., 52:6 (2011), 1124–1136  mathnet  crossref  mathscinet  isi
    13. K. Runovski, H.-J. Schmeisser, “Methods of trigonometric approximation and generalized smoothness. I”, Eurasian Math. J., 2:3 (2011), 98–124  mathnet  mathscinet  zmath
    14. Vakarchuk S.B. Doronin V.G., “Best Mean Square Approximations by Entire Functions of Finite Degree on a Straight Line and Exact Values of Mean Widths of Functional Classes”, Ukr. Math. J., 62:8 (2011), 1199–1212  crossref  mathscinet  isi
    15. S. B. Vakarchuk, V. I. Zabutnaya, “Jackson–Stechkin Type Inequalities for Special Moduli of Continuity and Widths of Function Classes in the Space $L_2$”, Math. Notes, 92:4 (2012), 458–472  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    16. Akgun R., “Approximation by Polynomials in Rearrangement Invariant Quasi Banach Function Spaces”, Banach J. Math. Anal., 6:2 (2012), 113–131  mathscinet  zmath  isi
    17. Vakarchuk S.B. Zabutnaya V.I., “On the Best Polynomial Approximation in the Space l (2) and Widths of Some Classes of Functions”, Ukr. Math. J., 64:8 (2013), 1168–1176  crossref  isi
    18. G. A. Yusupov, “Best polynomial approximations and widths of certain classes of functions in the space $L_2$”, Eurasian Math. J., 4:3 (2013), 120–126  mathnet
    19. M. R. Langarshoev, “Tochnye neravenstva tipa Dzheksona–Stechkina i znacheniya poperechnikov nekotorykh klassov funktsii v prostranstve $L_{2}$”, Model. i analiz inform. sistem, 20:5 (2013), 90–105  mathnet
    20. Shabozov M.Sh., Vakarchuk S.B., Zabutnaya V.I., “Sharp Jackson-Stechkin Type Inequalities for Periodic Functions in l-2 and Widths of Function Classes”, Dokl. Math., 88:1 (2013), 478–481  crossref  isi
    21. K. Tukhliev, “O priblizhenii periodicheskikh funktsii v $L_2$ i znacheniyakh poperechnikov nekotorykh klassov funktsii”, Model. i analiz inform. sistem, 22:1 (2015), 127–143  mathnet  mathscinet  elib
    22. S. B. Vakarchuk, “Generalized Smoothness Characteristics in Jackson-Type Inequalities and Widths of Classes of Functions in $L_2$”, Math. Notes, 98:4 (2015), 572–588  mathnet  crossref  crossref  mathscinet  isi  elib
    23. S. B. Vakarchuk, V. I. Zabutnaya, “Inequalities between Best Polynomial Approximations and Some Smoothness Characteristics in the Space $L_2$ and Widths of Classes of Functions”, Math. Notes, 99:2 (2016), 222–242  mathnet  crossref  crossref  mathscinet  isi  elib
    24. K. V. Runovskii, N. V. Omel'chenko, “Mixed Generalized Modulus of Smoothness and Approximation by the “Angle” of Trigonometric Polynomials”, Math. Notes, 100:3 (2016), 448–457  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    25. K. V. Runovski, “Trigonometric polynomial approximation, $K$-functionals and generalized moduli of smoothness”, Sb. Math., 208:2 (2017), 237–254  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    26. Vakarchuk S.B., “Jackson-Type Inequalities With Generalized Modulus of Continuity and Exact Values of the N-Widths For the Classes of (Psi, Beta)-Differentiable Functions in l-2. III”, Ukr. Math. J., 68:10 (2017), 1495–1518  crossref  mathscinet  isi  scopus
    27. Kolomoitsev Yu., “on Moduli of Smoothness and Averaged Differences of Fractional Order”, Fract. Calc. Appl. Anal., 20:4 (2017), 988–1009  crossref  mathscinet  zmath  isi  scopus
    28. M. Sh. Shabozov, A. A. Shabozova, “Nekotorye tochnye neravenstva tipa Dzheksona - Stechkina dlya periodicheskikh differentsiruemykh v smysle Veilya funktsii v $L_2$”, Tr. IMM UrO RAN, 25, no. 4, 2019, 255–264  mathnet  crossref  elib
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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